Exact quantum transport in non-Markovian open Gaussian systems

TL;DR

This paper develops an exact theoretical framework for analyzing heat, energy, and particle transport in non-Markovian Gaussian quantum systems, applicable to both fermionic and bosonic reservoirs, and capable of capturing transient dynamics and strong coupling effects.

Contribution

It introduces an effective non-Markovian master equation approach that enables calculation of heat statistics in arbitrary Gaussian systems with strong coupling and out-of-equilibrium conditions.

Findings

Recovery of Landauer-Büttiker results in weak-coupling steady state

Demonstration of transient negative heat conductance

Application to a prototypical fermionic system

Abstract

We build an exact framework to evaluate heat, energy, and particle transport between Gaussian reservoirs mediated by a quadratic quantum system. By combining full counting statistics with newly developed non-Markovian master equation approaches, we introduce an effective master equation whose solution can be used to generate arbitrary moments of the heat statistics for any number of reservoirs. This theory applies equally to fermionic and bosonic systems, holds at arbitrarily strong coupling, and resolves out-of-equilibrium transient dynamics determined by the system's initial state. In the steady-state, weak-coupling limit, we recover results analogous to those of the well-known Landauer-B\"{u}ttiker formalism. We conclude our discussion by demonstrating an application of the method to a prototypical fermionic system. Our results uncover a regime of transient negative heat conductance contingent upon the initial system preparation, providing a clear signature of non-trivial out-of-equilibrium dynamics.